Breadth is much more useful in most situations. But it's not like anyone really has a choice in that matter. If you play a game that engrosses you, of course you want to discover it as thoroughly as possible.

Also, the poll sucks as the 3rd option renders everything obsolete.

Well, I guess the question is: is both possible? 

Are there enough hours in the day to commit to hundreds of games AND to exhaust those hundreds of games?

I think I lean more towards breadth with a few select games that I know inside out. For example, I know a ridiculous amount of stuff related to Overwatch, watch gameplay analysis, streamers, coaches (Jayne is the best) but for most other games I'll do the main quest and move on.